Nasser al-Khelaifi appears fond of the phrase. It is short and punchy, and it serves as something of a mission statement for his presidency of Paris Saint-Germain. "We dream big," he says, on more than one occasion. Happily for him and the French capital's only major football club, dreams have the habit of coming true when they are supported by bundles and bundles of cash.

It is Wednesday afternoon and the stands at the rough-and-ready Parc des Princes are empty. The night before, they had teemed with passion and rampant joy as PSG made a triumphant return to the Champions League. The 4-1 victory over Dynamo Kyiv could scarcely have been scripted better. Zlatan Ibrahimovic and Thiago Silva, two of the highest-profile summer signings, got the opening goals while Javier Pastore, the marque purchase from the previous close season, got the final one. The trio cost €105m (£84m) in transfer fees alone.

Jean-Claude Blanc, the PSG director-general, wanders over, all dark velvet tailoring and Gallic style. "It was one of those nights when everything comes together," he says. He has been in sport for long enough to know that things are rarely this simple. "The highs are fleeting," he adds. "You feel the lows for longer." Khelaifi reinforces the sense of perspective. "Last night was just the first step," he says.

But these are heady days for the long-sleeping, rapidly-waking Parisian institution and there is no masking the sense of excitement. Since Khelaifi's Qatar Sports Investments took over 70% of the club's shares last summer, they have spent roughly a quarter of a billion euros on transfer fees. The most expensive purchase, Lucas Moura, at €45m (£36m), is yet to arrive, having been loaned back to São Paulo until the end of the year. Ezequiel Lavezzi, at €30m (£24m), was a mere substitute against Kiev.

"It's a simple message," Khelaifi says. "We are building a team to be one of the best in Europe. To become big, you need to sign players now and that is what we are doing. Obviously, we believe in our targets and objectives, and we are really confident that the dreams are going to come true."

Khelaifi's ambition is as rich as his company, which is the sports business arm of his native Qatar, the wealthiest nation, per capita, in the world, due to its natural gas reserves. The 38-year-old is suave, smart and seriously well connected. He goes back with the Crown Prince of Qatar, Tamim bin Hamad al-Thani, their friendship having been forged when they were tennis-mad boys. Khelaifi went on to play professionally and the pair would be teammates in the Qatar national team.

"I'm six years older than him," Khelaifi says, "and we first met when the crown prince was eight. We met through tennis, we used to play together. I have a good relationship with him."

Khelaifi is also the general manager of al-Jazeera Sport, the Qatar-owned TV station and, after the PSG takeover, the media outlet bought up a tranche of Ligue 1 broadcast rights, to emerge as competition to the previously dominant Canal Plus. Al-Jazeera has launched the subscriber channels beIN Sport 1&2 in France to screen its matches and Khelaifi is an emerging media rights player. He refused to comment on whether he would bid for the overseas rights to the Premier League when they became available.

The potential for a conflict of interest seems obvious; imagine if Sky owned Manchester United and the intrigue over fixture scheduling. There is another story to Khelaifi's al-Jazeera connection, which is that he is the employer of a pundit called Arsène Wenger. "He works with us for four or five years," Khelaifi says. "He's a fantastic guy, a great manager, also."

Khelaifi wanted Wenger to leave Arsenal last summer to replace the PSG manager Antoine Kombouaré and oversee QSI's five-year project. Wenger's commitment to Arsenal did not waver. It always felt as though Kombouaré was on borrowed time and, on 22 December, the day after PSG went top of Ligue 1, he was sacked or, to use Khelaifi's words, "we found a friendly agreement with him. He was happy with it, we were happy with it. I didn't give him the sack. We are gentlemen".

Carlo Ancelotti, the former Chelsea manager, was recruited and it was a disappointment that PSG finished the season as the runners-up to Montpellier, even if the objective of Champions League qualification, for the first time since 2004, was achieved. "Arsène Wenger doesn't want to leave Arsenal, he is very loyal to Arsenal," Khelaifi says. "We are very lucky to have Carlo. He is one of the best coaches in the world, if not the best."

Khelaifi smiles when it is put to him that he seems like a man in a hurry. "It's the same in all businesses," he says. "Forget yesterday, it's about getting the result today." His zeal to make an eyecatching impact was epitomised by his attempts to sign David Beckham from Los Angeles Galaxy last summer and Carlos Tevez from Manchester City in January.

"I met Beckham, I went over to Los Angeles," Khelaifi says. "We were honestly not far from a deal. He wanted [to come] … we wanted him but I think it was a family issue, his family. When I talked to him, he believed in our project, which is very important. It's not just about money. Even with Tevez, he wanted to come here. We didn't agree on the numbers that he wanted so it was very simple. We just didn't want to overpay."

It is incongruous to hear Khelaifi talk of not over-paying and the question that practically screams at him relates to how he can satisfy Uefa's financial fair play regulations. He details his strategy, of investing in the club's youth academy and his aim of finding and producing "the next Messi" in Paris. There are 20 million people, he notes, in the city and its surrounds, and only one major football club, which makes PSG "unique" and gives them a "big advantage".

His is a "complete project". He intends to market the club as an international brand and promote "new media" opportunities. There are plans to expand the Parc des Princes and build a training ground that will be "one of the best in the world". He stresses that revenues have increased under QSI, partly because of better sponsorship deals and more executive seating at the stadium. Attendances have risen.

"I respect all other clubs," Khelaifi says. "I just ask them to focus on themselves and their problems and we focus on our club and our problems. I am very confident that we will reach our goals and we will comply with financial fair play."

But the headline transfer spend figure cannot be accommodated easily. And this is before player wages are taken into account. Khelaifi says that Thiago Silva "is being paid the same salary that he got at Milan. We didn't over-pay by one euro. I think we are paying the market salaries."

On the other hand there is Ibrahimovic, who reportedly earns €14m-a-year (£11m)after tax, which means that the club are paying out roughly €30m-a-year (£24m)for one player.

The reality is that PSG need additional sponsorship. QSI is actively pursuing high-end deals and they will not rule out partnerships with Qatar-based companies. This raises the prospect of them following Manchester City, for example, in banking huge sums from organisations that have links to their ownership. City have a £400m sponsorship arrangement with Etihad Airways, which is owned by the Abu Dhabi government.

Khelaifi gives nothing away when pressed on where the extra sponsorship may come from while he also insists that there is no political basis for Qatar's investment in PSG. In the city of romantics, he prefers to reflect on his pride at Qatar being chosen to host the 2022 World Cup, and his sporting targets for PSG.

"We want to win the league for the next three years and we want to be competitive in the Champions League," Khelaifi says. The landscape of European football has changed again.